Project Summary Many clinical studies on survival outcomes based on observational data are challenged by unmeasured confounding. Instrumental variable (IV) methods are popular approaches for dealing with both measured and unmeasured confounding and are increasingly being adopted in clinical studies. The IV methods are very well developed for linear and some generalized linear regression models, however, the IV methods are not well developed for survival outcomes, especially for the Cox proportional hazards model which is the most popular regression model for censored survival data. Recently, there is a widespread use of two stage residual inclusion (2SRI) method offered by Terza et al. (2008) for nonlinear models, and 2SRI has been the method of choice for analyzing Cox model using IV in clinical studies. However, the causal parameter using 2SRI is only identified under a homogeneity assumption that goes beyond the assumptions of IV, and Wan et al. (2015) demonstrated that under standard IV assumptions, 2SRI could fail to consistently estimate the causal hazard ratio. In this proposal, we seek to develop a novel IV method to obtain consistent estimates of causal treatment effects for survival outcomes under standard IV assumptions, while accounting for unmeasured confounding and censoring. Specifically we will evaluate the effectiveness of postmastectomy radiotherapy (PMRT) on survival of breast cancer patients with 1-3 positive lymph nodes and tumors ? 5 cm (AJCC pT1-2pN1), a group of patients on whom the use of PMRT remains controversial. We expect that our project will have broad impact and wide applications in comparative effectiveness studies on survival outcomes, and our method will help clinical researchers improve their understanding about the potential risks and benefits of alternative treatments by obtaining trustworthy inference for survival data from observational studies.